Answer:
G=0.0728
Step-by-step explanation:
The expression given is:
This expression has the format of a compounded interest at a rate G for a time T. If B = 3,455, A = 1,969, and T = 8, the value of the rate G is determined by:
![3,455=1,969*(1+G)^8\\G = \sqrt[8]{\frac{3,455}{1,969}}-1\\G=0.0728](https://tex.z-dn.net/?f=3%2C455%3D1%2C969%2A%281%2BG%29%5E8%5C%5CG%20%3D%20%5Csqrt%5B8%5D%7B%5Cfrac%7B3%2C455%7D%7B1%2C969%7D%7D-1%5C%5CG%3D0.0728)
The rate G is 0.0728.
-14x + 14 = 8
A hot-air balloon has an 8-foot diameter that is changing at a rate of 14 foot per minute. How long in minutes, x, will it take until the balloon has a diameter of 14 feet?
We observe that when we clear x we have:
-14x = 14-8
-14x = 6
Which means that the balloon will not reach a diameter of 14 feet
We have the following equation:
<span> h(t)=-4.92t^2+17.69t+575
</span> For the domain we have:
<span> </span>We match zero:
-4.92t ^ 2 + 17.69t + 575 = 0
We look for the roots:
t1 = -9.16
t2 = 12.76
We are left with the positive root, so the domain is:
[0, 12.76]
For the range we have:
We derive the function:
h '(t) = - 9.84t + 17.69
We equal zero and clear t:
-9.84t + 17.69 = 0
t = 17.69 / 9.84
t = 1.80
We evaluate the time in which it reaches the maximum height in the function:
h (1.80) = - 4.92 * (1.80) ^ 2 + 17.69 * (1.80) +575
h (1.80) = 590.90
Therefore, the range is given by:
[0, 590.9]
Answer:
the domain and range are:
domain: [0, 12.76] range: [0, 590.9]
